A number of Katie Mitchell's productions for theatre have been rejected, with a tone approaching anger, by certain critics. Her Iphigenia at Aulis, staged at the National Theatre in 2004, was not one of them. Euripides's final play deals with the start of the Trojan war: the Greek generals assemble on the coast ready to set out across the sea to Asia, and they cannot do so until a child is sacrificed to ensure favourable winds. The truth is manipulated, specious arguments offered, humanity cynically set aside. The production, hailed as a classic, chimed grimly with events in the Middle East.

Subsequently Mitchell has directed Bach's St Matthew Passion at Glyndebourne, as well as working on Strindberg's Dream Play, Chekhov's The Seagull, an adaptation of Virginia Woolf's The Waves, and Martin Crimp's Attempts on Her Life, all at the National Theatre, where she is an associate director. Now, however, she has come back to Euripides, this time to Women of Troy, which opens at the National this week.

The play may be seen as a pendant to Iphigenia; it is not about the beginning of a war, but rather its ugly finish. The royal Trojan women, Hecuba and her daughters Andromache and Cassandra, and the beautiful Helen, cause of the conflict, are captives. Troy burns. In some gloomy holding area, the women await their fate. The play is a "what happened next?" to the bit-part players in the Iliad. The once noble Trojan women are forced to undergo humiliation and pain beyond endurance. Andromache's child Astyanax, not much more than a baby, is executed.

Mitchell makes the contemporary resonance clear: "It's the ultimate play about collateral damage ... about the horror of those people who get left behind after these huge military machines move through nations." The key idea, she contends, is "the collapse of moral certainty". The work could end up as a harrowing, ever more grotesque iteration of monstrosities, but, she says, "the real conflict is between these Greek officials and Trojan women ... how these civil servants cope with what their masters have done. They are now on the ground having to deal with collateral damage." She argues that the play is an articulation of Euripides's "rage" at contemporary events: the Athenians had, in 415BC, committed a horrifying outrage on the island of Melos, killing all the men and enslaving the women and children. "It's a very dangerous and frightening play," she says.

Mitchell is immensely serious - until she hoots with laughter, when she realises she has just said something more than usually earnest. She speaks in ready-made sentences, clearly punctuated, using words like "accurate", "precise" and "concrete" over again to describe her practice - which is striking, given that some critics have perceived in her work a willful disregard of playwrights' intentions. She cuts text drastically at times, in order, she argues, to communicate the ideas of plays more effectively. She has said: "I think it's a good idea to have your scissors to hand when you're about to direct Chekhov" - a sentiment not designed to endear her to purists. Audiences for Women of Troy may be surprised that the opening section of the play, in which the gods promise to punish the Greeks, has gone completely; indeed, she is working with less than half of the original text.

The largely negative critical reaction to her ruthless scissors-job on The Seagull (2006) left Mitchell "incredibly surprised. Martin Crimp" - the adapter - "and I worked for months on the material, very carefully, with a lot of respect for the writer, trying to find a way of making it live for audiences now, so that all the steps that happen would be psychologically credible. So it was a little ambush, the extremity of the response."

What she does is seen by some as an affront to an entire tradition of British theatre-making, with its time-honoured stage conventions and performance practice. "The question is whether you think theatre is performing and speaking words, or whether you think it's representing human behaviour," she says. "My interest is in being thorough about representing human behaviour and emotion. I love words, but I am not interested in doing live literary criticism."

Mitchell was born in 1964 and brought up in Hermitage, a village near Newbury, Berkshire. Her father is a dentist turned book designer, her mother ran a restaurant and a charity. She has a brother who is a photographer. Theatre was not much thought about in her house, though her great-grandfather was in the music hall with Fred Karno - said to be the originator of the custard-pie-in-the-face gag - and Charlie Chaplin, and her great-grandmother was a high-kicking dancer in the Tiller troupe. As a teenager Mitchell wanted to be an artist, but had settled on theatre by the time she was 16. She studied English literature at Magdalen College, Oxford, fitting in as much acting and directing as she could. Afterwards, she found a job typing up scripts at the King's Head theatre in Islington and later worked with Paines Plough and the Royal Shakespeare Company.

The most important influence in Mitchell's artistic development has been theatre from eastern Europe. While a student at the Edinburgh festival she encountered work by the Polish artist and director Tadeusz Kantor; then, in London, she saw pieces by Russian directors Lev Dodin and Anatoly Vasilyev, and the Polish company Gardzienice, which was strongly influenced by the early work of director Jerzy Grotowski. As a teenager Mitchell had also immersed herself in classic Russian literature and later in film - Klimov and Sheptiko as well as Tarkovsky. On a trip to Russia in 1989 she watched Dodin and Vasilyev working and became very interested in Stanislavsky - mainly because the work was "so precise. Very concrete, very precise, and it was a matter of learning to watch what actors do with laser eyes and to help them become immersed in a situation to play a character in a real time, in a real place, so an audience could believe that the action was really happening."

She began to use "these tools, but not in an informed way; and I stumbled around for many years". A turning point came in 1999, when she began to study with Tatiana Olear, an actress who had trained under Dodin, and with Elen Bowman, whose own training came in a direct line from Stanislavsky.

This translates into a very particular modus operandi. With every text that she works on, she reads it first (with the cast) for things that are "facts, non-negotiable facts: it is Russia; there is Moscow; Arkadina married Gavril Treplev". Then, "all the grey areas you put down as a list of questions. You have to be aware that you might have affinities that might take you in subjective directions." The process at this point is diagnostic, almost scientific, rather than interpretative, she says. Mitchell and her cast will do exhaustive research, building the histories of the characters and studying the background to the text and writer. The point is to avoid "over-subjective, therapeutic connections", to produce a "cool, steady analysis" that will lead to an understanding of the "machine of the text" and its main ideas. The key themes of Women of Troy, she says, are "war, family, collapse of moral certainty and death. Lovely themes!"

Next comes interpretation: "It's like adjusting or fine-tuning on a complex machine. You can never turn off the volume on one of the ideas of the play, but you can adjust it; for instance, I might lower the volume of 'family' in the articulation of this play today. It is confusing that people have a picture of me smashing things up for the sake of it. That isn't the case. The first step I take is careful consideration and detailed study of the material, then I work out how to communicate it now."

Because of the specificity of her process, Mitchell tends to work with the same core of collaborators. "It will normally take one performance for an actor to use the process efficiently," she says. Those who have seen more than one of her productions will note obvious relationships between them: one could see, for example, how her The Waves and Attempts on Her Life were related, and also The Seagull and Jephtha (for Welsh National Opera). "In my head I work through strings of shows. But there might come a point, with something like The Waves, when I just drop all these tools; the work preceding it had probably reached a ceiling and we needed to look for new ways of communicating ideas, so we started to look at video, image, voiceover and sound." For the actors to retain authenticity, perhaps she needs to keep pushing them to the edge of their capabilities, throwing out the accustomed ways of working and inventing new ones, so that the work doesn't end up turning into a "style".

Her commitment to psychological realism is such that she asked the actors in Iphigenia to keep in character when they were off-stage; and for Women of Troy, certain characters have literally been "diagnosed": Mitchell and the team have worked with a psychiatrist who has offered the notion that Cassandra has manic depression (some sufferers believe they can predict the future, though presumably not with Cassandra's total accuracy). He has also likened Helen of Troy to Diana, Princess of Wales, and Marilyn Monroe; thus, for the purposes of this production, Mitchell has made Helen bulimic. In the past she has also studied the physical manifestations of emotion, in order to represent them on stage more accurately. She compares her practice to that of a "maker of bespoke tables".

She names Pina Bausch and Siobhan Davies as choreographers she admires. The influence of the former is particularly clear; Mitchell has used a lot of social dance such as tango and foxtrot in productions - and the chorus in Women of Troy does the quickstep. These dances appeal "because they are couple-dancing. I find that a very beautiful metaphor for relationships, or the breakdown of relationships."

Given her rigorous attempt to rid productions of traditional stage conventions, it is no surprise that Mitchell pauses when I ask what theatre she likes to go to. Having reminded me that she has a two-year-old daughter, which means that evenings out are less frequent than they used to be, she says: "For me performance isn't necessarily about going to the theatre - it could be about going to an exhibition or an opera or some dance ... When I do go to the theatre I am like a child, waiting to lose myself in an imaginary world." It happens all-too rarely.